The first compiler was written by Grace Hopper in 1952 while the Lisp interpreter was written in 1958 by John McCarthy's student Steve Russell. Writing a compiler seems like a much harder problem than an interpreter. If that is so, why was the first compiler written six years before the first interpreter?

Writing a compiler seems like a much harder problem than an interpreter.

That might be true today, but I would argue that it was not the case some 60 years ago. A few reasons why:

With an interpreter, you have to keep both it and the program in memory. In an age where 1KB of memory was a massive luxury, keeping the running memory footprint low was key. And interpreting requires a bit more memory than running a compiled program.

Modern CPUs are extremely complex with huge catalogs of instructions. So writing a good compiler is truly a challenge. Old CPUs were much simpler, so even compilation was simpler.

Modern languages are much more complex than old languages, so even compilers are much more complex. Old languages would thus have simpler compilers.

Numerous computers in the 1950s used front panel switches to load instructions and the output was simply rows of lamps/LEDs. Hobbyists even used front-panel switches and LEDs into the 1970s. Maybe you're familiar with the infamous Altair 8800.

Other hardware limitations also made interpreters unfeasible. There was the extreme limited availability of primary memory (e.g. RAM) in computers in the 1950s. Prior to the semiconductor integrated circuit (which didn't come until 1958) memory was limited to magnetic core memory or delay line memory which was measured in bits or words, no prefix. Combined with the slowness of secondary storage memory (e.g. disk or tape), it would be considered wasteful, if not unfeasible to have much of the memory used for the interpreter, even before the program being interpreted was loaded.

Memory limitations were still a major factor when the team lead by John Backus at IBM created the FORTRAN compiler in 1954-57. This innovative compiler was successful only because it was an optimizing compiler.

Most of the computers in the 1950s barely had any Operating System, let alone modern features such as dynamic linking and virtual memory management, so the idea of an interpreter was too radical and impractical at that time.

Addendum

The languages of the 1950s were primitive. They included only a small handful of operations, often influenced either by the underlying hardware's instructions or the problem definition of their targeted use.

At that time, computers were rarely general purpose computers in the sense that we think of computers today. That they were reprogrammable without having to be rebuilt was considered a revolutionary concept—previously people had been using electromechanical machines (typically calculators) to compute or calculate answers (the majority of applications in the 1950s were numeric in nature).

From a Computer Science point of view, compilers and interpreters are both translators, and roughly equal in complexity to implement.

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